Search NASA⌕ Search

SEARCH · Search NASA

Results for “vector spaces”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

A Computational Efficient Space-Vector Modulation Scheme for A Hybrid Seven-Level Converter for Medium Voltage Grid-Tied Applications

In this paper, a fast space-vector modulation (SVM) scheme is proposed for a hybrid 7-level (7-L) converter, i.e., cascaded T-type converter and H-bridge converters, for grid-tied applications. Using oblique coordinate reference, the proposed SVM can quickly locate the switching triangle enclosing the reference vector in the 7-L space vector diagram. Then all available switching sequences and vector duty cycles are acquired by straightforward calculation without using any look-up tables, which significantly reduces the computational cost. The floating capacitor voltages are also stabilized by using the proposed SVM. Experimental studies on a scale-down prototype are presented in this work to validate the effectiveness of the proposed scheme.

Diao, Fei↗

A Digital Three Level Space Vector Modulator for High Frequency Vector Sequence Generation

This letter proposes a digital high-speed three-level space vector pulse width modulator (3L-SVPWM). A conventional 3L-SVPWM is typically computation-based, involving a sequential execution of sub-tasks on a digital signal processor (DSP) based controller. The resulting high computation time of 5.4 μs limits the implementation of additional control blocks for switching frequencies greater than 100 kHz. This is overcome by transforming sub-tasks into digital blocks with 1-0 decisions and simpler arithmetic operations. The sub-task blocks are executed concurrently on a programmable logic device (PLD). Hence, a fast 3L-SVPWM execution in 140 ns is achieved. The proposed digital 3L-SVPWM enables high switching frequency operation of wide bandgap (WBG) device-based 3 L inverters to generate high fundamental frequency waveforms. A finite state machine is an integral part of the proposed implementation with the ability to generate any vector sequence, maximizing the usage of redundant vector states in 3L-SVPWM. Here, the proposed digital 3L-SVPWM operation is demonstrated with a GaN-based 3 L active neutral point clamped (3L-ANPC) inverter. Experimental results are presented at 250 kHz switching frequency to generate vector sequences for center-aligned SVPWM (CA-SVPWM) and common mode voltage reduced SVPWM (CMVR-SVPWM). The results also showcase a high fundamental frequency generation capability of 10 kHz.

active neutral point clamped inverter↗

A Virtual Space Vector Model Predictive Control for a Seven-Level Hybrid Multilevel Converter

This paper proposes a virtual space vector (VSV) model predictive control (MPC) for a three-phase seven-level (7L) hybrid multilevel converter (HMC), where each phase consists of an active-neutral-point-clamped converter with a floating H-bridge. To achieve the best current tracking, which is the primary goal of the proposed algorithm, a novel geometrical positioning approach is proposed to select the optimal voltage vector among all the realspace vectors and VSVs. Then, all the possible switching sequences that belong to the optimal voltage vector are evaluated to realize the dc capacitor voltage balancing and common-mode voltage reduction. Through an external modulator, the optimal voltage vector can be synthesized by using either one-, three-, or seven-segment switching sequence. Compared with the conventional MPC, the proposed VSV-MPC can reduce not only the computational burden but also the current THD. Both simulation and experimental results obtained on silicon carbide based 7L-HMC prototype are presented to validate the feasibility and effectiveness of the proposed VSVMPC strategy.

42 ENGINEERING↗

A Six-Phase Space Vector PWM Technique for Wide Bandgap Device-Based Three-Level Inverters

This article presents a space vector pulsewidth modulation (SVPWM) technique for wide bandgap (WBG) device-based three-level (3L) six-phase inverters. Implementation of the SVPWM techniques for any six-phase inverter is complex for its high number of possible voltage vectors. Different six-phase load configurations are also possible depending on the angle between two consecutive phases and neutral point connections. The implementation techniques change depending on the load configuration. Moreover, a common neutral point for all six phases leads to circulating currents. Capacitor voltage balancing is also needed for 3L inverters. Capacitor voltage balancing and addressing the circulating current problem further increases the implementation complexity. In this article, a generalized SVPWM technique is proposed for the six-phase 3L inverters that is implementable using two three-phase 3L SVPWM blocks. The SVPWM technique also ensures dc bus capacitor voltage balancing and minimizes circulating current. Here, the SVPWM technique is experimentally verified using a GaN-based 3L six-phase active neutral point clamped (ANPC) inverter prototype, and the results are presented in this article.

42 ENGINEERING↗

A Simple Space Vector Modulation of High-Frequency AC Linked Three-Phase-to-Single-Phase/DC Converter

High frequency (HF) ac linked converter functions well to interface between buses with different voltage types. Using a three-phase-to-single-phase matrix converter, a single-phase cyclo converter, and a HF transformer, we can compose a HF ac linked converter to interface between three-phase ac grids and single-phase ac or dc distributed generations (DGs). In this paper, a novel space vector modulation (SVM) method is proposed for such kind of converter. The proposed SVM method converts the mains three-phase ac voltage to a HF ac voltage at the primary side of transformer, and then unfolds the HF ac voltage to a single-phase ac or dc voltage at the secondary side of transformer. Without need to compute separate switching signals for the primary and secondary converters and then coordinate their operations elaborately, the proposed SVM method can be easily implemented by incorporating the HF chopping into the SVM of traditional indirect matrix converter. Therefore, no complicated duty cycle computation or elaborate switching states combination is required. Simulation and hardware-in-loop implementation demonstrate the validity of the proposed method.

42 ENGINEERING↗

Online adaptive basis refinement and compression for reduced-order models via vector-space sieving

In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs). However, there is no a priori assurance that these approximate solutions are accurate; their accuracy depends on the ability of the low-dimensional trial basis to represent the FOM solution. As a result, ROMs can generate inaccurate approximate solutions, e.g., when the FOM solution at the online prediction point is not well represented by training data used to construct the trial basis. To address this fundamental deficiency of standard model-reduction approaches, this work proposes a novel online-adaptive mechanism for efficiently enriching the trial basis in a manner that ensures convergence of the ROM to the FOM, yet does not incur any FOM solves. The mechanism is based on the previously proposed adaptive $h$-refinement method for ROMs, but improves upon this work in two crucial ways. First, the proposed method enables basis refinement with respect to any orthogonal basis (not just the Kronecker basis), thereby generalizing the refinement mechanism and enabling it to be tailored to the physics characterizing the problem at hand. Second, the proposed method provides a fast online algorithm for periodically compressing the enriched basis via an efficient proper orthogonal decomposition (POD) method, which does not incur any operations that scale with the FOM dimension. We report these two features allow the proposed method to serve as (1) a failsafe mechanism for ROMs, as the method enables the ROM to satisfy any prescribed error tolerance online (even in the case of inadequate training), and (2) an efficient online basis-adaptation mechanism, as the combination of basis enrichment and compression enables the basis to adapt online while controlling its dimension.

42 ENGINEERING↗

Generating accurate density matrices on the tangent space of a Grassmann manifold

Interpolating a density matrix from a set of known density matrices is not a trivial task. This is because a linear combination of density matrices does not necessarily correspond to another density matrix. In this Communication, density matrices are examined as objects of a Grassmann manifold. Although this manifold is not a vector space, its tangent space is a vector space. As a result, one can map the density matrices on this manifold to their corresponding vectors in the tangent space and then perform interpolations on that tangent space. The resulting interpolated vector can be mapped back to the Grassmann manifold, which can then be utilized (1) as an optimal initial guess for a self-consistent field (SCF) calculation or (2) to derive energy directly without time-consuming SCF iterations. Such a promising approach is denoted as Grassmann interpolation (G-Int). The hydrogen molecule has been used to illustrate that the described interpolated method in this work preserves the essential attributes of a density matrix. For phosphorus mononitride and ferrocene, it was demonstrated numerically that reference points for the definition of the corresponding tangent spaces can be chosen arbitrarily. In addition, the interpolated density matrices provide a superior and essentially converged initial guess for an SCF calculation to make the SCF procedure itself unnecessary. Finally, this accurate, efficient, robust, and systematically improved G-Int strategy has been used for the first time to generate highly accurate potential energy surfaces with fine details for the difficult case, ferrocene.

Chemistry↗

Root-N Krylov-space correction vectors for spectral functions with the density matrix renormalization group

In this work, we propose a method to compute spectral functions of generic Hamiltonians using the density matrix renormalization group (DMRG) algorithm directly in the frequency domain, based on a modified Krylov-space decomposition to compute the correction vectors. Our approach entails the calculation of the root-N (N=2 is the standard square root) of the Hamiltonian propagator using Krylov-space decomposition and repeating this procedure N times to obtain the actual correction vector. We show that our method greatly alleviates the burden of keeping a large bond dimension at large target frequencies, a problem found with conventional correction-vector DMRG, whereas achieving better computational performance at large N. We apply our method to spin and charge spectral functions of t-J and Hubbard models in the challenging two-leg ladder geometry and provide evidence that the root-N approach reaches a much improved spectral resolution compared to the conventional correction vector.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A resolution independent neural operator

The Deep operator network (DeepONet) is a powerful yet simple neural operator architecture that utilizes two deep neural networks to learn mappings between infinite-dimensional function spaces. This architecture is highly flexible, allowing the evaluation of the solution field at any location within the desired domain. However, it imposes a strict constraint on the input space, requiring all input functions to be discretized at the same locations; this limits its practical applications. Here, in this work, we introduce a general framework for operator learning from input–output data with arbitrary number and locations of sensors. This begins by introducing a resolution-independent DeepONet (RI-DeepONet), enabling it to handle input functions that are arbitrarily, but sufficiently finely, discretized. To this end, we propose two dictionary learning algorithms to adaptively learn a set of appropriate continuous basis functions, parameterized as implicit neural representations (INRs), from correlated signals defined on arbitrary point cloud data. These basis functions are then used to project arbitrary input function data as a point cloud onto an embedding space (i.e., a vector space of finite dimensions) with dimensionality equal to the dictionary size, which can be directly used by DeepONet without any architectural changes. In particular, we utilize sinusoidal representation networks (SIRENs) as trainable INR basis functions. The introduced dictionary learning algorithms are then used in a similar way to learn an appropriate dictionary of basis functions for the output function data, which defines a new neural operator architecture referred to as the R esolution I ndependent N eural O perator (RINO). In the RINO, the operator learning task simplifies to learning a mapping from the coefficients of input basis functions to the coefficients of output basis functions. We demonstrate the robustness and applicability of RINO in handling arbitrarily (but sufficiently richly) sampled input and output functions during both training and inference through several numerical examples.

Deep operator network (DeepONet)↗

A double copy from twisted (co)homology at genus one

We study the twisted (co)homology of a family of genus-one integrals — the so called Riemann-Wirtinger integrals. These integrals are closely related to one-loop string amplitudes in chiral splitting where one leaves the loop-momentum, modulus and all but one puncture un-integrated. While not actual one-loop string integrals, they share many properties and are simple enough that the associated twisted (co)homologies have been completely characterized [1]. Using intersection numbers — an inner product on the vector space of allowed differential forms — we derive the Gauss-Manin connection for two bases of the twisted cohomology providing an independent check of [2]. We also use the intersection index — an inner product on the vector space of allowed contours — to derive a double-copy formula for the closed-string analogues of Riemann-Wirtinger integrals (one-dimensional integrals over the torus). Similar to the celebrated KLT formula between open- and closed-string tree-level amplitudes, these intersection indices form a genus-one KLT-like kernel defining bilinears in meromorphic Riemann-Wirtinger integrals that are equal to their complex counterparts.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Simple and Robust Carrier-Based PWM Technique for Single-Stage Three-phase Rectifier Indirect Matrix Converter

Indirect matrix converters (IMC) can offer high efficiency, high power density, and bidirectional power flow capability with a single-stage three-to single-phase AC-AC power conversion integrating a conventional three-phase active rectifier with a primary side full-bridge inverter of a dual active bridge converter. However, the IMCs generally require space vector modulation techniques, leading to complex sectors and dwell times calculations. A practical implementation of the modulation methods with a commonly used digital signal processor becomes even more challenging when considering power factor correction, harmonics reduction, and deadtime between sector transitions. This paper proposes a simple and robust carrier-based pulse width modulation (PWM) technique determined through a voltage-source inverter (VSI) to current-source inverter (CSI) to IMC conversion. This translation enables the adoption of all conventional VSI control methods with active and reactive power control in the IMCs through simple carrier and reference waveform comparison. The VSI vectors are first one-on-one matched with CSI vectors and translated to IMC modulation signals without calculating sectors and dwell times. Nine different carrier waveforms are proposed, and the converter performance is analyzed. Grid current THD and efficiency are estimated for each modulation method. The symmetric A and B methods had the lowest THD of the grid current, 2.80%, and the efficiency remained at approximately 98.3%, making it the most suitable carrier-based method proposed in this paper. The space vector PWM (SVPWM) modulation method was implemented to the DSP and generated the expected twelve gate signals.

Benson, Mikayla↗

Reliability Improvement by Fault-Tolerant Operation of NPC Inverter for Motor Driving

The high-reliability operation of three-level inverters is crucial to prevent equipment damage, process downtime, and economic losses. This article investigates a three-level neutral-point-clamped inverter under all possible combinations of open-circuit and short-circuit faults and proposes a new postfault operation method without adding extra hardware. This method provides comprehensive solution for operations after single and multiple-device failures, increasing the inverter reliability by 24%. This article classified postfault modulations and uncovered previously unknown fault scenarios that can be addressed using the proposed control method. A new postfault modulation based on space vector modulation with virtual vectors is proposed. The feasibility of the proposed control method is verified by simulation and an experiment for one fault scenario in a three-level neutral-point-clamped inverter with a 3.73 kW motor load. Furthermore, this article contributes to improving the reliability of three-level inverters.

42 ENGINEERING↗

Replacing non-biomedical concepts improves embedding of biomedical concepts

Embeddings are semantically meaningful representations of words in a vector space, commonly used to enhance downstream machine learning applications. Traditional biomedical embedding techniques often replace all synonymous words representing biological or medical concepts with a unique token, ensuring consistent representation and improving embedding quality. However, the potential impact of replacing non-biomedical concept synonyms has received less attention. Embedding approaches often employ concept replacement to replace concepts that span multiple words, such as non-small-cell lung carcinoma, with a single concept identifier (e.g., D002289). Also, all synonyms of each concept are merged into the same identifier. Here, we additionally leveraged WordNet to identify and replace sets of non-biomedical synonyms with their most common representatives. This combined approach aimed to reduce embedding noise from non-biomedical terms while preserving the integrity of biomedical concept representations. We applied this method to 1,055 biomedical concept sets representing molecular signatures or medical categories and assessed the mean pairwise distance of embeddings with and without non-biomedical synonym replacement. A smaller mean pairwise distance was interpreted as greater intra-cluster coherence and higher embedding quality. Embeddings were generated using the Word2Vec algorithm applied to a corpus of 10 million PubMed abstracts. Our results demonstrate that the addition of non-biomedical synonym replacement reduced the mean intra-cluster distance by an average of 8%, suggesting that this complementary approach enhances embedding quality. Future work will assess its applicability to other embedding techniques and downstream tasks. Python code implementing this method is provided under an open-source license.

algorithms↗

First Order Transport of a Cold Uniform Ellipsoid of Charge

A single particle has a 6-element phase space vector $s = (x, γv)$ where $γv =\frac{p}{m}$ s proportional to the relativistic momentum. The ellipsoid is represented by a 21-element vector $(s, C, V)$ where $s$ is the phase space location of the centroid. $C$ is the 3 × 3 covariance matrix defined by $C_{ij} = ⟨δx_iδx_j⟩$, where $δx$ is the distance of a particle from the centroid $x$. $C$ is symmetric so only counts as 6 elements of the overall vector. $V$ is a general 3 × 3 matrix that determines the velocity distribution in the bunch by $δ(γv) = Vδx$. In total this makes 6 + 6 + 9 = 21 elements.

43 PARTICLE ACCELERATORS↗